25 mice were involved in a biology experiment involving exposure to chemicals found in ciggarette smoke. 15 developed at least 1 tumor, 9 suffered re[iratory failure, and 4 suffered from tumors and had respiratory failure

Following is the area model of 27 x 7 = 189.

An area model is a rectangular graphic used in mathematics to multiply and divide two numbers or expressions.

The length and breadth of the rectangle are determined by the factors, also known as the quotient and divisor. In other words, you can divide a large area (in this case, a 23 37 rectangle) into smaller ones, calculate the areas of each separately, and then sum them to determine the overall area.

Write the enlarged form of each factor first. Next, sketch your model. To determine the area of each smaller rectangle, multiply next. To find the entire area, add those items last.

            20                  7

7           140                 49

27 × 7 = 140 + 49 = 189

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Answer:

(x,y) = (-1/4, -5/4)

Step-by-step explanation:

To solve the system of equations using the substitution method, we can start by solving one equation for one variable in terms of the other. Let's start by isolating y in the first equation:

y = -3x - 2

Now we can substitute this expression for y into the second equation:

6x - 2(-3x - 2) = 1

Simplifying this, we get:

6x + 6x + 4 = 1

12x + 4 = 1

12x = -3

x = -3/12 = -1/4

Now we can substitute this value of x back into the first equation to solve for y:

y = -3(-1/4) - 2 = 3/4 - 2 = -5/4

So the solution of this system of equations is (x,y) = (-1/4, -5/4)

You can check this solution by substitute these values back into the original equation and check that both are correct.

Tell me if this helped :)

Answer:

( - [tex]\frac{1}{4}[/tex], [tex]\frac{-5}{4}[/tex] )

Step-by-step explanation:

Substitute -3x - 2 for y

6x - 2y = 1

6x -2(-3x - 2) = 1

6x + 6x + 4 = 1  Combine like terms

12x + 4 = 1  Subtract 4 from both sides

12x + 4 - 4 = 1 - 4

12x = -3  Divide both sides both sides by 12

[tex]\frac{12x}{12}[/tex] = [tex]\frac{-3}{12}[/tex]

x = - [tex]\frac{1}{4}[/tex]

Substitute - [tex]\frac{1}{4}[/tex] for x to solve for y

y = -3x - 2

y = (-3)[tex]\frac{-1}{4}[/tex] - 2

y =[tex]\frac{3}{4}[/tex] - 2

y = [tex]\frac{3}{4}[/tex] - [tex]\frac{8}{4}[/tex]

y = [tex]\frac{-5}{4}[/tex]

The estimated regression equation is :

          ŷ = 12.924 - 3.682[tex]x_{1}[/tex] + 45.216[tex]x_{2}[/tex]

S0, option(d) is the correct answer.

In statistics, an estimated regression equation is an equation constructed to model the relationship between dependent and independent variables.

The least squares method is the most widely used method for developing estimates of the model parameters.

For simple linear regression, the least squares estimates of the model parameters β0 and β1 are indicated [tex]b_{0}[/tex] & [tex]b_{1}[/tex]. Using these approximates, an estimated regression equation is constructed: ŷ = [tex]b_{0} + b_{1} x[/tex] . The graph of the estimated regression equation for simple linear regression is a straight-line approximation of the relationship between y and x.

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The meaning of the y-intercept in this situation is ,

''For every additional mile the cab travels, the total fee increases by $12.00.''

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

From the table, we have the following parameters:

Points (x, y) = (2, 5) and (15.00, 19.50)

So, we would calculate the slope as follows:

Slope = (19.50 - 5)/(15.00 - 2)

Slope = 14.50/13

Slope = 1.11

Hence, We get;

Fixed fee = $15 - (1.12 x 2)

               = $15 - 2.24 ≈ $12.00

So, We get;

For every additional mile the cab travels, the total fee increases by $12.00.

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Answer: ≈2.32

Step-by-step explanation: So, we can solve this in 2 ways:

1) 12.75 / 5.5 (easiest way)

= 2.3181818181818183

(Rounded to the nearest hundredth) ≈ 2.32

2) Set up a proportional relationship:

[tex]\frac{12.75}{5.5}[/tex] = [tex]\frac{?}{1}[/tex]

Now, divide 12.75 by 5.5, and get about 2.32

Now, let's check our answer:

2.32 x 5.5 = 12.76

So, he paid about 2.32 per pound.

I hope this helped!

Therefore , the solution of slope intercept comes out to be X intercept for the function is x = - 1

In math, the intersection is where the line's slope intersects the y-axis. a point on a line or curve where the y-axis crosses. The formula for the linear line is given as Y = mx+c, whereby m denotes the slope и c the y-intercept. In the intercept form of the equation, the line's slope (m) and y-intercept (b) are highlighted. The slope and y-intercept of an equation with the intercepting form (y=mx+b) are m and b, respectively. There are several equations that can be rewritten to appear to be slope detections. The slope and como are both modified to 1 if y=x is translated as y=1x+0, for example.

Here,

It is the point where a line or curve crosses the X axis

The function f(x) = x³ + x² - 6x = c

Let, y = f(x) = x³ + x²- 6x -c =0

at the X intercept, y = 0,

so, 0 = x³+ x²- 6x -6

x²(x +1) - 6(x +1) =0

(x +1) ( x²-6) = 0

x = -1, x = √6

X intercept is x = -1

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The degree of the given polynomial is 5.

A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

Given is a polynomial, 4x²y³-2x²+7y-8

We know that, A polynomial of two variable x and y, like ax^ry^s is the algebraic sum of several terms of the prior mentioned form, where r and s are possible integers.

Here, the degree of the polynomial is r+s where r and s are whole numbers.

Therefore, in the given polynomial, the degree will be

4x²y³

Taking the powers,

2+3 = 5

Hence, the degree is 5

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Answer:

D

Step-by-step explanation:

all around of side are 360 degree that's why only pentagon has 360 degree

The set of ordered pairs that best represents the linear function f(x) = (1/2)x +2 is the third option.

H { (-4, 0), (-1, 1.5), (2, 3), (4, 4)}

We want to see which one of the given sets best represents the linear function:

f(x) = (1/2)x +2

To identify the correct option, we need to see which set of ordered pairs only includes points that are on the linear equation.

For example, the first set starts with the point (-4, -7.5)

Replacing these values in our function we will get:

-7.5 = (1/2)*-4 + 2

-7.5 = -2 + 2

-7.5 = 0

This is false, so we can discard the first equation.

(We also can see that f(-4) = 0, so we can also discard the second option).

Now let's look at the third option, the second point is (-1, 1.5)

f(-1) = 1.5 = (1/2)*-1 + 2

        1.5 = -0.5 + 2

         1.5 = 1.5

This point belongs to the functions graph.

(and on the other set we have the point (-1, 3), that point clearly does not belong to the graph, so we can also discard this option).

Finally, the only remaining option is the third one, H.

{ (-4, 0), (-1, 1.5), (2, 3), (4, 4)}

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Answer: $77

Step-by-step explanation:

Using the given expression, we can find the total cost for all the tickets.

The question asks for the cost of 3 adults and 4 children.

Let's substitute the values for the variables(again).

We'll get

15*3+8*4(since there's 3 adults and 4 children)

= 45+32

= 77

Total: $77

Nice airpods, btw

The circumference of a circle with a given diameter of 15 inches is equal to 15pi which is equal to 47.12 inches.

The circumference of a circle is the distance around the edge of the circle.

The formula for calculating the circumference of a circle is given by,

C = 2πr = πd

Where C is the circumference, π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle and d is the diameter.

It is also known as the perimeter of the circle.

In the question above, we're given,

Diameter of the circle (d ) = 15 inches.

So, using the formula for the circumference of the circle,

Circumference (c) = π d

                              = π * 15

                              = 47.12 inches

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Answer:

follow me if this helped you

Step-by-step explanation:

Area of inscribed square.

A circle is inscribed into a square, find the area of the circle if one side of the square is 15 m

The diameter of the inscribed circle is equal to the length of the square's diagonal, which is equal to the length of one side of the square multiplied by the square root of 2 (since the diagonal of a square is equal to the square root of 2 times the length of one side). Therefore, the diameter of the inscribed circle is 15m * sqrt(2) = 15m * 1.41421356237 = 21.213203435596424m

The area of a circle is given by the formula A = π * r^2, where r is the radius of the circle. Since the diameter of the circle is 21.213203435596424m, the radius is half of that, which is 10.60660171779821m.

So the area of the circle is A = π * r^2 = π * 10.60660171779821^2 = 353.09

Answer: No Solution

Step-by-step explanation:

There is no solution.

A set of equations with the same slopes and different y-intercepts have no solution.

Answer:

Angle FSM = 92°  OPTION B

Step-by-step explanation:

[tex]5x+32=7x+8[/tex]

[tex]5x-7x=8-32[/tex]

[tex]-2x=-24[/tex]

[tex]x=\frac{-24}{-2} =12[/tex]

Angle FSM:

[tex]FSM=7x+28=7(12)+8=84+8=92[/tex]

Hope this helps

Answer: x = -2

Step-by-step explanation: Divide each side by factors that do not contain the variable to isolate it.

For estimation, she have to make calculation as 320x50/

Using one significant figure as an example 3692 should be converted to one square foot (s.f.). The number 3 is the first significant digit because it is the first non-zero digit.6 exceeds 5 in number.We round up because 6 is greater than 5 One plus three equals four, and 3692 is four thousand square feet.

each number to the nearest significant figure.Use the 'approximately equal to' symbol to build the new estimated calculation.Consider units when calculating and use the rounded numbers to provide an approximation.

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The values of x for which f(x) = g(x) - 2 are given as follows:

x = 1 and x = 2.

The functions for this problem are defined as follows:

The equation is given as follows:

f(x) = g(x) - 2.

Replacing the values, we have that:

x² - 2x - 1 = x - 1 - 2

x² - 2x - 1 = x - 3

x² - 3x + 2 = 0.

We can factor the equation as follows:

(x - 2)(x - 1) = 0.

Hence the solutions are obtained as follows:

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The numerator of the indicated expression is s+7.

The numbers 7, 14, 21, 28, 35, and 42 are the multiples of 7. 3 and 7 only share 21 as their smallest common number. 21 is the least common denominator as a result. The denominators can be multiplied by one another to find the common denominator for two or more fractions.

We were given the following rational expression:

where p is the numerator and q is the denominator, is the general representation of the rational expression.

So, the expression we provide is:

Assuming the LCM, the following expression can be rewritten as

Comparing (1) with the above-mentioned general rational expression

The numerator of the given expression is p=s+7.

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Therefore , the solution of the given problem of triangle comes out to be a=6 and b=17.

An triangle is a polygon since it has four or more parts. It is a simple geometric shape. A square having angles A, B, and C is referred to as a triangle ABC. When the sides are not collinear, Euclidean geometry generates a single plane and square. If a triangle has three sides and three corners, it is a polygon. The corners of a triangle are where its three sides meet. The sum of the angles in a triangle is 180 degrees.

Here,

Given : A right triangle ,

=> 8²+a²= 10²

=> a² = 100 -64

=>  a² =36

=> a =6

For b,

=> b²  = 8² + 15²

=> b²  = 64 + 225

=> b² = 289

=> b = 17

Therefore , the solution of the given problem of triangle comes out to be a=6 and b=17.

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The value for the proportional constant, for given data, is 5/6.

A linear function is a function that, when plotted, creates a straight line. Typically, it is a polynomial function with a maximum degree of 1 or 0. Nevertheless, calculus and linear algebra are also used to represent linear functions.

Given that b  varies directly as m

so b ∝ m

it says b is directly proportional to m,

removing the proportional sign apply a constant k,

b = km

where k is the proportional constant,

and m = 6 and b = 5

5 = 6k

k = 5/6

Hence the value of the constant is 5/6.

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Six Flags:

1,473/3 = 491 people per hour.

Hershey Park:

944/2 = 472 people per hour.

Six Flags has more people in the first hour. Six Flags has 19 more people than Hershey Park.

491>472

I hope this helps you!!

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

[tex]\qquad \sf  \dashrightarrow \: f(x) = 2 {x}^{2} - 2x - 4[/tex]

[tex]\qquad \sf  \dashrightarrow \: f(3) = 2(3) {}^{2} - 2(3) - 4[/tex]

[tex]\qquad \sf  \dashrightarrow \: f(3) = 2(9) {} - 6- 4[/tex]

[tex]\qquad \sf  \dashrightarrow \: f(3) = 18{} - 10[/tex]

[tex]\qquad \sf  \dashrightarrow \: f(3) = 8[/tex]

Answer:

the solution and explanation/work is in the images

Answer:

x+5 > 12

Step-by-step explanation:

A number plus 5 is greater than 12 represents x + 5 > 12.

The yard is an English unit of length in both the British imperial and US customary systems of measurement equalling 3 feet or 36 inches.

Since 1959, it has been precisely standardised to 0.9144 metres per international agreement. The word "yard" comes from the Old English word "gerd," "gyrd," etc., which was used for measuring sticks, staves, and branches.

The term first appears in the late 7th-century regulations of Ine of Wessex  where "yard of land" refers to the yardland, an ancient English tax assessment unit equivalent to one-fourth of a hide.

Around the same time, it was substituted for a branch moved by the wind in the Lindisfarne Gospels description of the messengers from John the Baptist in the Gospel of Matthew. In addition to the yardland, surveying lengths of 15 feet (4.6 m) or 16.5 feet were also referred to as "yards" in Old and Middle English (5.0 m).

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Answer:The correct statement among the given options is:

StartFraction 1 inch Over 2.54 centimeters EndFraction = StartFraction 7 inches Over 17.68 centimeters EndFraction SO 1 is the answer.

The required vertices of hyperbola is given as (3, 5±√38).

Hyperbola is part of conic section, and its equation is given as,
[tex](x - h)^2/a^2 + (y - k)^2/b^2 = 1[/tex], where h,k is center and a and b are the lengths of the semi-major and the semi-minor axes.

Here,
Given equation of hyperbola,
36x²-y^²-216x+10y+261=0
Equation of hyperbola in vertex form is given as,
(x - 3)²/(19/18) - (y - 5)²/38 = 1

From above equation,
h = 3 k = 5 a = √38/6 and b = √38

Vertices of the  hyperbola is given as,
(h, k ± b) = (3, 5±√38)

Thus, the required vertices of hyperbola is given as (3, 5±√38).

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Given the number lines (attached) the correct one is Option B) because it represents the right placement of values.

A number line is a depiction of a graded straight line that serves as a visual representation of real numbers in primary mathematics. Every point on a number line is presumed to be a real number, and every real number is assumed to be a point.

We can tell that option B is correct because:

Thus, option B is correct in the given number line.

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The number of bears, b is 300 for the company has to sell in one day to equal its daily cost.

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

A toy company spends $1800 per day for factory expenses plus $9 to make each teddy bear.

And, They sell the teddy bears for $15 a piece.

Let number of bears for the company has to sell in one day to equal its daily cost = b

Hence, We can formulate the inequality as;

⇒ 15b = 9b + 1800

Solve for b;

⇒ 15b - 9b = 1800

⇒ 6b = 1800

⇒ b = 300

Thus, There are 300 teddy bears has to sell in one day.

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Answer:

C

Step-by-step explanation:

If you have a grade of 54.96 and you take a summative test worth 80%, it would bring up your grade by the following calculation:

New grade = (54.96) + (80/100) * (100 - 54.96)

New grade = 54.96 + (0.8) * (45.04)

New grade = 54.96 + 36.032

New grade = 90.992

So, your new grade would be 90.992

It's worth noting that this calculation assumes that the summative test is worth 80% of your overall grade, and that your previous grade was 54.96 out of 100. If this isn't the case, the result will be different.